A260617 Three-dimensional array read by shells: S(i, j, k) = i + j + k; i >= 0, j >= 0, k >= 0.

0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 2, 3, 4, 3, 4, 5, 4, 5, 6, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 5, 6, 7, 8, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 9, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 6, 7, 8, 9, 10

Offset: 1

Author

Matthew Campbell, Sep 17 2015

Keywords

• nonn

Comments

The triples (i,j,k) are ordered first by maximal coordinate, and then lexicographically. - Charlie Neder, Dec 23 2018

Examples

			S(0, 0, 0) = 0 + 0 + 0 = 0.
S(0, 0, 1) = 0 + 0 + 1 = 1.
S(0, 1, 0) = 0 + 1 + 0 = 1.
S(0, 1, 1) = 0 + 1 + 1 = 2.
S(1, 0, 0) = 1 + 0 + 0 = 1.
S(1, 0, 1) = 1 + 0 + 1 = 2.
S(1, 1, 0) = 1 + 1 + 0 = 2.
S(1, 1, 1) = 1 + 1 + 1 = 3.
S(0, 0, 2) = 0 + 0 + 2 = 2.
...
		

Links

• Charlie Neder, Table of n, a(n) for n = 1..1000
• Matthew Campbell, Coordinate Pattern

Programs

Python

s = lambda x,y,z : x+y+z # function for 3d array
i = 1
for n in range(0,10):
  for x in range(0,n+1):
    for y in range(0,n+1):
      if (x!=n and y!=n):
        print(i, s(x,y,n))
        i += 1
      else:
        for z in range(0,n+1):
          print(i, s(x,y,z))
          i += 1
# Charlie Neder, Dec 26 2018

Extensions

Definition clarified by Charlie Neder, Dec 25 2018